The 2D real time optimally adapting meshes (ROAM) algorithm has had wide success in the field of terrain visualization, because of its efficient error-controlling properties. In this paper, we propose a generalization of ROAM in 3D suitable for scalable volume visualization. Therefore, we perform a straightforward 2D/3D analogy, replacing the triangle of 2D ROAM by its 3D equivalent, the tetrahedron. Although work in the field of hierarchical tetrahedral meshes was widely undertaken, the produced meshes were not used for volumetric rendering purposes. We explain how to compute a bounded error inside the tetrahedron to build a hierarchical tetrahedral mesh and how to refine this mesh in real time to adapt it to the viewing conditions. We further show how to achieve cell sorting in linear time, thus yielding real time view-dependent display of the volumetric object. We present examples of large volume data sets and compare our approach with a similar one. Our results outline the high quality and computational efficiency of our approach.